Listen to Robert Emmerich introduce The Big Apple, a hit song from 1937. Music written by Bob and performed by Tommy Dorsey's Clambake Seven with Bob on piano. Lyrics written by Buddy Bernier and sung by Edythe Wright. Audio provided by Dorothy Emmerich.

"Cold as a witch’s tit” (or “colder than a witch’s tit") is very cold. The expression has variations that include other things associated with a witch. “Cold as a witch’s kiss” was cited in print in 1918. “Cold as a witch’s tit” was cited in print in 1932. “Cold as a witch’s eye” was cited in 1933 and “cold as a witch’s lips” in 1956.

Jerome Weidman’s I’ll Never Go There Any More (1941) specifically mentioned New York City:

“You have to expect heat in New York in the summer no matter where you are. But wait till the wintertime comes. It’ll be as cold as a witch’s tit.”

12 June 1918, Rockford (IL) Register-Gazette, “The Confessions of a German Deserter,” pg. 9, col. 4:
The inside of a cloud is cold as a witch’s kiss, but it is fun shooting into them and then suddenly out into the clear sky again.

Google News Archive
4 October 1933, Miami (FL) Daily News, “Scribe Assigned To Crash World Series Gate Finally Gets In—On Ticket” by James H, Street (AP), pg. 9, col. 3:
The man at the player’s entrance had a look as cold as a witch’s eye.

Google BooksI’ll Never Go There Any More
By Jerome Weidman
New York, NY: Simon and Schuster
1941
Pg. 58:
“It’s the summer. You have to expect heat in New York in the summer no matter where you are. But wait till the wintertime comes. It’ll be as cold as a witch’s tit.”

Old Fulton NY Postcards
26 August 1956, The Sunday Press (Binghamton, NY), “Bus Seat Hog Is Called The Most Swinish of All,” pg. 9-A, col. 7:
Give the seat hog a look as cold as a witch’s lips or a tentative shove and he or she stares back menacingly, but moves not a muscle and pigheadedly stays put.

Google BooksNone But the Brave
By Freida Kenyon Brown
New York, NY: Crown Publishers
1958
Pg. 83:
Who in God’s name, he thought, could have predicted a night like this, this early in the fall? Black as hell and cold as a witch’s teat!

Google BooksThe Basic Training of Pavlo Hummel:
A Play
By David Rabe
New York, NY: Samuel French
1969
Pg. 56:
MICKEY. They send you to Georgia for the winter and it’s like a witch’s tit. Can you imagine that? A witch’s tit? Eeeeeeggggggg. Put ice on your tongue. That ever happens to me, man, I’d turn in my tool.

,a href="http://books.google.com/books?id=HrAfAAAAQBAJ&pg=PA178&dq=witch’s+teat&hl=en&sa=X&ei=FXyRUs980ciwBM3LgMAB&ved=0CEwQ6AEwBji0AQ#v=onepage&q=witch’s%20teat&f=false">Google Books
Idiom Structure in English
By Adam Makkai
The Hague: Mouton & Co.
1972
Pg. 178:
Thus it is said of somebody who is idle that he won’t even lift a finger, extreme cold is described as cold as a witch’s tit or cold enough to freeze the balls off a brass monkey. These forms are often vulgar and listed as slang in the Dictionary of American slang.